The bottom of a light house and bottom of the mast of two ships are on the same straight line and the angles of depression from the light house at the bottom of mast of two ships are `60^(@) and 30^(@)` respectively. If the distance of the points at the bottom of the light house and the bottom of the mast of first ship is 150 metres, calculate how far will the mast of the other ship from the light house be and what will the height of light house be.

Explanation

Let AB be the light house and D and C are the bottom of the masts of two ships and BD
= 150 metres.
Now, from the right-angled triangle ABC, we get,
`tan60^(@) = (AB)/(BD) " "or, " " sqrt(3) = (AB)/(150) " " or, " " AB = 150sqrt(3)`
`tan 30^(@) = (AB)/(BC) " " or, " " (1)/(sqrt(3) = (AB)/(BC)`
or,` " " BC = sqrt(3)AB = sqrt(3) xx 150sqrt(3) = 450`
Hence the distance of other ship from the light house is 450 metres and the height of the light house is `150sqrt(3)` metres.